The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" describes a study that investigated the usefulness of MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were reviewed. Of the 650 women, 13 had breast cancer, and the MRI exam detected breast cancer in 12 of these women. Of the 637 women who did not have breast cancer, the MRI correctly identified that no cancer was present for 547 of them. The accompanying table summarizes this information. Breast Cancer Present Breast Cancer Not Present Total MRI Indicated Breast Cancer 12 90 102 MRI Did Not Indicate Breast Cancer 1 547 548 Total 13 637 650 Suppose that an MRI exam is used to decide between the two hypotheses. H0: A woman does not have breast cancer. Ha: A woman has breast cancer. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) a. One possible error would be deciding that a woman who has breast cancer is cancer-free. Is this a Type I error or a Type II error? a. Type I b. Type II b. Use the information in the table to approximate the probability of this type of error. (Hint: See Example 10.8. Enter your probability as a fraction.) c. There is a second type of error that is possible in this context. Describe this error. a. In this scenario, a Type I error is concluding that a woman has cancer when she really does not have cancer. b. In this scenario, a Type II error is concluding that a woman has cancer when she really does not have cancer. Use the information in the table to approximate the probability of this type of error. (Enter your probability as a fraction.)

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Description: The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" describes a study that investigated the usefulness of MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were revi

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Section: Chapter Questions

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The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" describes a study that investigated the usefulness of MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were reviewed. Of the 650 women, 13 had breast cancer, and the MRI exam detected breast cancer in 12 of these women. Of the 637 women who did not have breast cancer, the MRI correctly identified that no cancer was present for 547 of them. The accompanying table summarizes this information.

Breast Cancer Present	Breast Cancer Not Present	Total
MRI Indicated Breast Cancer	12	90	102
MRI Did Not Indicate Breast Cancer	1	547	548
Total	13	637	650

Suppose that an MRI exam is used to decide between the two hypotheses.

H₀: A woman does not have breast cancer.

H_a: A woman has breast cancer.

(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)

One possible error would be deciding that a woman who has breast cancer is cancer-free. Is this a Type I error or a Type II error?

a. Type I

b. Type II

Use the information in the table to approximate the probability of this type of error. (Hint: See Example 10.8. Enter your probability as a fraction.)

There is a second type of error that is possible in this context. Describe this error.

a. In this scenario, a Type I error is concluding that a woman has cancer when she really does not have cancer.

b. In this scenario, a Type II error is concluding that a woman has cancer when she really does not have cancer.

Use the information in the table to approximate the probability of this type of error. (Enter your probability as a fraction.)

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